## Linear Operators: Spectral operators |

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Page 2197

Let B be a complete ( o - complete ) Boolean algebra of projections in the B -

space X and let { Ea } be a monotone generalized

Ea } is ...

Let B be a complete ( o - complete ) Boolean algebra of projections in the B -

space X and let { Ea } be a monotone generalized

**sequence**( a monotone**sequence**) in B . Then , if { Ex } is increasing , lim Eqx = ( V Ec ) , « ex , while if {Ea } is ...

Page 2218

Let { Ex } be a weakly convergent generalized

its limit E is a projection . It must be shown that { Ea } converges strongly to E . By

Lemma 6 , E is in B and so a consideration of the

...

Let { Ex } be a weakly convergent generalized

**sequence**in B and suppose thatits limit E is a projection . It must be shown that { Ea } converges strongly to E . By

Lemma 6 , E is in B and so a consideration of the

**sequence**{ Ea – E } shows that...

Page 2450

4 there exists a complete orthonormal basis { { n } consisting of eigenvectors of T .

We let Tun = dn Xn , and suppose that none of the eigenvalues dn is multiple (

that is , that the

4 there exists a complete orthonormal basis { { n } consisting of eigenvectors of T .

We let Tun = dn Xn , and suppose that none of the eigenvalues dn is multiple (

that is , that the

**sequence**{ n } contains no repetitions ) and that do 70 for n 2 1 .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

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